Determine the Real Solutions to the System of Nonlinear Equations $$2 x ^ { 2 } + y ^ { 2 } = 17$$

question 194

Multiple Choice

Determine the real solutions to the system of nonlinear equations.
- $$2 x ^ { 2 } + y ^ { 2 } = 17$$
$3 x ^ { 2 } - 2 y ^ { 2 } = - 6$

• A) \(( 2,3 ) , ( 2 , - 3 ) , ( - 2,3 ) , ( - 2 , - 3 )\)
• B) \(( 1,3 ) , ( 1 , - 3 ) , ( - 1,3 ) , ( - 1 , - 3 )\)
• C) \(( 1,3 ) , ( - 1 , - 3 )\)
• D) \(( 2 , - 3 ) , ( - 2,3 )\)

---

Definitions:

Rebuttable Presumption

is a presumption in law that one can challenge and overturn with evidence to the contrary.

Breach of Duty

Failure to meet the standard of care or obligation required by law or contract, which could lead to legal action.

Pure Comparative Negligence

A legal doctrine under which damages in an accident are calculated based on the degree of fault of each party, allowing a plaintiff to recover even if they are 99% at fault, but the recovery is reduced by the plaintiff's level of fault.

Negligence

The failure to take reasonable care to avoid causing injury or loss to another person.